In the usual connection between two subscriber's modems using the telephone network, the subscriber's digital data must be translated into analog tones for transmission over the local loop to and from the telephone network. At each subscriber's modem, the received analog waveform is sampled and quantized by a high precision analog to digital (A/D) converter and at a sufficiently high sampling rate to avoid aliasing distortion. For the symbols transmitted over the channel to be reasonably free of intersymbol interference over the frequency spectrum used by the symbols, the modems employ adaptive filters called equalizers. When the channel is properly equalized, symbols preceding and following the symbol of interest contribute nothing to that signal, i.e., there is no inter-symbol interference at the moment when the signal of interest is sampled. The channel response that needs to be equalized includes the loop resistance, the anti-aliasing filter, the hybrid circuit, and any analog and digital filters that may be present in the signal transmission/receiving path. Equalization is accomplished by passing the digital signal through an adaptive filter whose tap coefficients are adjusted in a direction opposite to the derivative of the mean square error signal for that tap. This method is also referred to as the least mean squared (LMS) method of adaptation and is well understood in such textbook literature as Bernard Widrow's "Adaptive Signal Processing".
However the public switched telephone network is not quite transparent to the transmitted symbols because a limited precision A/D converter is employed at the network interface to the local loop so that the digital signal presented to the adaptive filter includes whatever error was introduced because of the difference between the network codec's limited set of discrete slicing levels and the actual amplitude of the received analog signal. The amplitude difference to the nearest quantization level is called the quantization error. This error in .mu.-law and A-law pulse-coded modulation (PCM) codecs is different for each amplitude of transmitted signal. As a result, the response that needs to be equalized includes the quantization error characteristics of the network A/D converter, as well as that of the physical channel, e.g., the subscriber loop. While the response of the subscriber loop can be reasonably well modeled with a linear response over the voice band, important non-linear impairments are present in the A/D and D/A converters. It has been observed that A-law or .mu.-law PCM encoding introduces about 37-38 dB of quantization noise. This quantization noise sets an upper limit to the transmission speeds obtainable using traditional modem modulation techniques, such as CCITT V.34. U.S. Pat. No. 5,394,437 describes a high speed client modem which minimizes the effects of quantization noise by having its sampling times synchronized with, and its slicing levels the same as, those of the network PCM codec.
With the rapid proliferation of Internet communications, an even higher speed of operation is achievable for connections through the public switched telephone network between an Internet service provider's server modem and a subscriber's modem. Because most Internet service providers (ISPs) connect to the public switched telephone network using a digital line, such as T-1, data coming from an ISP need undergo no analog-to-digital conversion and therefore remains free of quantization noise. At the user's side interface to the subscriber's loop, a linear codec which has an SNR of 80-90 dB performs analog-to-digital conversion and the analog signal reaching the subscriber's modem is equalized in the usual manner. The result--in theory, at least--is throughput as high as 56 kbps in the "downstream" direction from the ISP to the client modem. Such higher speed operation is not, however, achievable in the "upstream" direction from the customer's modem to the server modem because the network .mu.-law or A-law PCM codec limits the SNR of the received signal to 37-38 dB and therefore the achievable speed.